Transitional Structures with Continuous Variations in Atomic Positions from Anatase to Rutile Improve Photocatalytic Activity

TiO2 polymorphs have distinct properties that are widely employed in various applications. However, mechanisms of transformations between these polymorphs are not fully understood, especially at atomic scale, inhibiting advancing the design and application of the transitional phases. Here, based on results from semi‐in situ transmission electron microscopy, density functional theory, and X‐ray photoemission experiments, a physical picture of transitional structures is discovered, in which continuous variations in atomic positions form along a previously unreported anatase‐to‐rutile phase transformation path of [010]A–to–[ 1¯1¯1$\overline 1 \overline 1 1$ ]R and (004)A–to– (011)R. These gradient structures give rise to continuous band bending, which promotes electron‐hole separation and inhibits their recombination across the bulk of the particles, leading to a large functionally active volume fraction and resulting in high photoactivity. These findings suggest that interphase matter based on extended gradient structures can be designed to advance new functions not achievable using abrupt interfaces.


Introduction
Polymorphs have been extensively employed in various applications due to their distinct properties. [1] For example, α-Al 2 O 3 has www.advmatinterfaces.de phase with the lowest activation barrier. The process of rutile nucleation and growth involves displacement of one-half the Ti atoms and rupture of 7 out of 24 TiO bonds in the unit cell, respectively, [16a] keeping the orientation relationship of 〈010〉 A -to-〈110〉 R and {112} A -to-{010} R . The {101} R twin structures and equivalent orientation relationship of 〈110〉 A -to-〈011〉 R and {112} A -to-{100} R were found in anatase polycrystalline powder [17] after the ART. Most of these studies are based on the investigation of aggregated particles by postmortem experiments, which are limited by the technical challenges of tracking and imaging a single anatase particle at the atomic scale at high temperatures (> ≈1000 °C). [16b,18] Particle rotation, morphological evolution, and interface migration among different particles during the high-temperature treatment in these studies obscure the ART process as such. These issues are generic to a broad range of polymorphic transformations. Accordingly, the atomic scale understanding of their mechanisms is in its infancy.
Here we track the evolution of single crystal and reveal atom rearrangement mechanisms in 3D during the ART process at atomic scale using double tilt transmission electron microscopy (TEM) heating holder (up to 1100 °C) and semi-in situ measurements protocols. We discover transitional phases, which are highly stable at room temperature and facilitate rapid electronhole separation, thus providing an atomic-level insight into the exceptionally high photoactivity of P25, and paving the way for the design of extended functional metastable structures.

Anatase [010] A to Rutile [111] R Transformation
The activation energy of the ART process for aggregated nanoparticles was shown to be significantly lower than that of a single crystal particle. [10c] Separate small anatase particles could be stable up to 1000 °C. [18] Therefore, we use a high temperature of 800-1100 °C to activate the phase transformation process of a single particle. The as-synthesized anatase nanorods, elongated along the [001] A direction (Figure 1a; Figure S1, Supporting Information), are formed by aggregation of ≈5 nm nanoparticles with slight misalignment, as indicated by diffuse diffraction spots (Figure 1d). After heating at 800 °C for 20 min, the nanorod transforms into a single crystal (Figure 1b) in the [010] A zone axis (as shown by sharp diffraction spots in Figure 1e). After an additional 20 min heating at 900 °C, the anatase nanorod transforms into a spherical rutile particle (Figure 1c). In this process, [010] A transforms to [111] R , as determined using the fast Fourier transform (FFT) diffraction patterns (DPs) obtained from the high resolution TEM (HRTEM) images (Figure 1a- (Figure 1l-n). Notably, all anatase particles elongated along the [001] A direction were found to transform into the rutile phase via the same pathway.

Formation of Gradient Structure and Twin Interfaces
Our semi-in situ TEM experiments demonstrate that local structure evolves from anatase to intermediate phases, which constitute a gradient structure over tens of nanometers, i.e., a structure with continuous variations of atomic positions (Figure 2a, see also Scanning TEM (STEM) images below), distinct from known crystalline TiO 2 phases. Based on our Density functional theory (DFT) simulations (see below), these structures possess anatase-like arrangement of the TiO bonds ( Figure 2c). We denote such gradient structures as "anatise" (AI), which reflects both the anatase-like local atomic arrangements and spatial variations of the lattice parameters. The angle (β) between (200) A and (004) A in the cell of AI (C AI ) varies from 90° to ≈88° (Figure 2a), approaching β' (85.8°) of the rebuilt crystalline rutile cell (C R ) shown in Figure 2b. Parameters c and β of C AI are in the ranges of 9.2-9.8 Å and 85-91°, respectively, based on measurements of numerous samples (Figure 3b). We observed the formation of similar anatise phases during transformation of TiO 2 -B to anatase. [20] In both cases, the anatise phase was found to be stable at room temperature for more than a year. Similarly, we define the structures that possess rutile-like TiO bonds as rutise (RI). We also observe transitional phases near rutile regions, corresponding to rutise structures ( Figure S2e,f, Supporting Information).
Using HRTEM imaging, we observe Ti 2 and Ti 4 in the anatase structure displacing by ¼[100] A after heating at 900 °C for 1 min, thereby forming an anatise phase, represented by C AI (Figure 2a

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Information) shows an example of a twin structure, in which both sides of the grain boundary are transformed to the rutile phase.
To determine the atomic structure of the anatise phase and its electronic properties, we performed the atomic-scale modeling of the ART established experimentally ( Figure 2). The details of the TiO bond arrangements, stability of anatise, and deformation-dependent density of states were examined using ab initio (DFT) simulations and the periodic model approach (see Experimental Section). The structural configurations forming the ART path were approximated using a linear interpolation C(t) = (1-t)C A + tC R , where t is a dimensionless parameter (0≤t≤1). Then, this path was refined via energy minimization with respect to the internal coordinates of all oxygen atoms and lattice parameters (see Supporting Information (SI) for details) for t varied between 0 and 1 with increments of 0.1.
As the value of t increases, TiO 2 retains anatase-like arrangement of the TiO bonds up to t = 0.8, where the deformation energy reaches ≈0.62 eV per TiO 2 formula unit (f.u.) ( Figure 3a). When t>0.8, oxygen atoms spontaneously rearrange into the rutile-like configuration. This persistence of the deformed anatase (anatise phase) in the wide range of t is reflected in the variations of the lattice parameters along the ART path (Figure 3b). In particular, the c parameter decreases continuously from ≈9.55 Å (t = 0) to ≈9.10 Å (t = 0.8) and then increases abruptly to 9.95 Å as anatise transforms to rutise. Similarly, angle β decreases continuously from 90° (t = 0) to ≈84° (t = 0.8) before abruptly changing to ≈86°, which also marks the transition to the rutise phase. This abrupt change of the TiO bonding pattern is consistent with our experimental observation that rutile forms via a sudden change from anatise once a certain temperature is reached and maintained long enough for the system to overcome the bond switching barrier (e.g., 950 ± 50 °C for ≈30 min; see Supporting Information for details). The switch from anatise to rutise requires breaking and reforming one out of six bonds in each TiO 6 octahedron, accompanied by changes of structural parameters, corresponding to reconstructive phase transformation, i.e., an isochemical change of a crystal structure, in which chemical bonds are broken and reformed. [21] We note that the ranges of c and β calculated for the entire span of the simulated anatise (0≤t≤0.8) and rutise (0.8<t≤1.0) phases are in a good agreement with the experimentally measured c and β ranges in multiple regions of the thermally processed samples (Figure 3c). This comparison allows us to assign a local magnitude of the deformation parameter t to each analyzed region of the samples.
The transformation from anatase to anatise is a displacive transformation, during which only bond length or bond angles change. [21] The supercell volume shows only little variation, indicating that a variety of anatise structures, as defined by specific values of 0<t≤0.8 (Figure 3d), can co-exist in a single TiO 2 particle without inducing volume change. In contrast, transition to rutise is associated with a significant volume reduction (t>0.8, Figure 3d). This observation suggests that if the particle morphology and interfacial constrains are such that TiO 2 particles transform under isochoric conditions (i.e., the total volume of  Table S1 (Supporting Information). Sim: simulation, Exp: experiment.
www.advmatinterfaces.de the sample remains constant), then, the transition to the rutise phase is suppressed, leaving anatise the dominant phase. Our results suggest that the phase transformation can originate at multiple locations within the crystals ( Figure S4c-i, Supporting Information), inducing polydomains of anatise structures that deform to different extents, as defined by specific local values of t, and lock in strain distributions that retain metastable anatise structures. Trapping strained metastable structures has been reported, for example, in frequently observed fivefold twins and grain-boundary-rich nanoparticle assemblies. [22] Since the potential energy profile (Figure 3a) was calculated for the infinite periodic TiO 2 bulk system, it neither captures the effects of morphology nor describes interactions of anatise structures with their surroundings and, therefore, does not show an energy minimum. We also note that this ART path, as represented by the parameter t, is only one of many possible paths the anatase-to-rutile transformation can take. It is well established that standard generalized-gradient approximation functionals, including Perdew-Burke-Ernzerhof (PBE), incorrectly predict anatase to be more stable than rutile. This deficiency can be mitigated by applying more accurate but more computationally demanding methods, such as the adiabatic connection fluctuation-dissipation theory with the random phase approximation (ACFDT-RPA). [23] We compared the potential energy profiles calculated using PBE and ACFDT-RPA (see Section S4, Supporting Information) for details) and found that they show similar trends ( Figure S5, Supporting Information).
Simulated XRD patterns for the anatise (t < 0.5) and rutise (t > 0.8) phases, which are most often observed in experiments, are similar to the anatase and rutile XRD, respectively ( Figure  S6, Supporting Information). Since anatise is effectively a con-tinuous field of the anatase lattice distortions, its quasi-periodic atomic positions result in the broadening of the anatase XRD peaks only and not in the formation of a new XRD pattern of its own (see Figure 4j). Instrument resolution further contributes to the XRD peak broadening but the effect is similar to the as-synthesized anatase and processed anatise particles. [24] Therefore, experimental XRD patterns cannot distinguish anatise from anatase phases.

Photoactivity Tests
The coexistence of anatase and anatise is also observed in samples of anatase after heat treatment in air (700 °C for 20 min and 120 min) and P25 and confirmed by high resolution high angle annular dark field scanning TEM (HAADF-STEM) images (Figure 4a-i), which are widely used to identify atomic positions in crystal structures, [25] demonstrating that they readily form and remain stable in thermally treated anatase.
The continuous variation of the atomic positions from anatase to anatise within one grain (Figure 2a)-defined as an "anatase" grain-could introduce continuous electronic structure changes that improve photocatalytic properties. To investigate this possibility, we prepared samples with various volume fractions of anatase, anatise, and rutile (Figure 4a-i and Table 1) by heating precursor anatase nanoparticles that are ≈5-10 nm square bipyramids elongated along <001> A , i.e., similar to those used in the semi-in situ experiments. These precursors were subjected to thermal treatment at 700 °C for 20 min and 120 min in air. In addition, P25 TiO 2 , a mixture of ≈70-85 wt. % anatase and ≈15-30 wt. % rutile, [1a,5,6] was also  Figure S4, Supporting Information) images of these samples show that anatise structures form in the "anatase" grains. Using the area of anatise structures in the HRTEM images, we estimate their volume fractions to be ≈6%, 39%, 64%, and 74% in the as-prepared, 700 °C/20 min, 700 °C/120 min, and P25 samples, respectively (Table 1).
We point out that these anatise structures formed in air are indistinguishable from the anatise structures observed in the semi-in situ TEM experiments discussed above (compare Figures 2a and 4a-i). Given similar morphology of the precursor anatase particles and the same intermediate and the resulting rutile phases (Figures 2b and 4j), we conclude that anatase TiO 2 follows the same phase transformation path in the air as in the semi-in situ TEM experiments. EELS spectra show no evidence of oxygen vacancies, which are typically manifested as an electron charge trapped on the Ti 3d states ( Figure S9, Supporting Information), i.e., vacancy concentration is below EELS detection limit. Comparing structures in Figures 2 and 4 suggests that even if vacancies are formed under vacuum, their effect must be limited to the phase transformation barrier and rate but does not affect the resulting structures.
We note that there is a similarity between the structural motifs in P25 and in the heat-treated anatase samples. In particular, we observe the same twin interfaces in P25 and in the thermally treated TiO 2 and find that the number (e.g., 8 or 12) of (004) planes of anatise in P25 lattice structures is a multiple of the number (4) of (004) planes in one C AI (Figures S2b and S4d, Supporting Information), corresponding to the phase transformation process as observed in our ART experiments. Therefore, the anatise structure observed in our thermally treated samples may serve as a good model to investigate structurefunction relationship of P25.
To explore catalytic behavior of these samples, we analyzed the photoactivity for 700 °C/20 min and 700 °C/120 min samples. for both samples, the methylene blue degradation rates were enhanced by ≈1.7 times even though their surface area decreased by 3 and 5 times, respectively, in comparison to that of the as-prepared anatase sample (Figure 4k; Figure S7a-e, Supporting Information). The results of the water splitting test show consistent improvement of the photocatalytic activity (Figure 4k; Figure S7f-i, Supporting Information). Photocatalytic activity of materials is closely associated with surface area, morphology, heterointerface, and phase. [26] The 700 °C/20 min and 700 °C/120 min samples have larger particle sizes and smaller surface areas than as-prepared anatase; however, their photocatalytic activities are higher than that of anatase ( Figure 4k and Table 1). In addition, we examine the morphologies (exposed surfaces) of as-synthesized anatase, 700 °C/20 min and 700 °C/120 min samples, and P25. We find that {101}, the most energetically stable surface (0.44 J m −2 ), [27] is the dominating surface of all anatase nanoparticles ( Figure S4j-m, Supporting Information). This termination is consistent with our thermal treatment: heating typically induces growth of the most stable surfaces. Twin boundaries were shown to generate "back-to-back" electrostatic potential drops, which facilitate charge separation and transport. [28] Among 69 inspected particles in 700 °C/120 min and P25 samples, we find only ≈12% of them have twin boundaries. Therefore, we do not expect that surface area, morphology, or twin interfaces enhance photo activity of TiO 2 (Figure 4k). Grain boundaries and defects often serve as recombination centers for electrons and holes. [29] Therefore, we can rule them out as the origin of photoactivity enhancement. Since previous reports pointed out that anatase-rutile interfaces enhance photoactivity, we quantified the density of these interfaces. We found that out of 90 randomly selected interfaces between nanoparticles in P25 (30% rutile and 70% anatase), only ≈11% were anatase-rutile interfaces ( Figure S8, Supporting Information). In addition, previous reports suggest that anatase powder isolated from P25, i.e., containing no anatase-rutile interfaces at all, shows comparable or sometimes even higher photoactivity than P25. [5] Therefore, anatase/rutile interfaces alone cannot be the origin of such high photoactivity of P25. Furthermore, electron energy loss spectroscopy (EELS) spectra provide no evidence for oxidation state variation (e.g., the presence of Ti 3+ ) in the samples ( Figure S9, Supporting Information). Therefore, we propose that this enhancement of photoactivity is associated with the formation of the anatise phase and differences in the intrinsic structures of anatase and anatise (Figure 4; Figure S4, Supporting Information).

Continuous Band Bending Induced by Gradient Structures
The increase of the photoactivity upon thermal treatment of TiO 2 samples and the existence of the gradient structures in both P25 and heat-treated samples suggests that these structures are responsible for the enhanced photocatalytic activity. To reveal the atomic-scale origin of the activity, we link the anatise structure and the corresponding electronic structure. To this end, we consider the anatase supercell subjected to inhomogeneous deformation as defined by C(t) and two deformation parameters t 1 and t 2 , in general t 1 ≠ t 2 (Figure 5a), that mimics continuous deformation field observed in the gradient structures. To capture the effect of structural differences between regions represented by t 1 and t 2 on their electronic properties, we Table 1. Composition, surface area, and particle size of TiO 2 samples. The anatise powder XRD pattern is indistinguishable from that of anatase (Figure 4j; Figure S6g, Supporting Information); therefore, its volume fraction was estimated using HRTEM imaging (see also Supporting Information for details). Rutile phase fraction was estimated based on the intensity of rutile {110} and anatase {101} peaks in XRD spectra (Figure 4j). [30] Samples As prepared 700 °C 20 min 700 °C 120 min P25 www.advmatinterfaces.de calculate the density of states (DOS) and determine spatial variations of the valence band (VB) maximum (E V ) and conduction band (CB) minimum (E C ) by projecting the DOS on the orbitals of atoms located in each of the 16 planes of the supercell. An example of the band edges for t 1 = 0.2 and t 2 = 0.8 demonstrates that both E V and E C in anatise (t 2 = 0.8) shift to higher energy with respect to that of weakly distorted anatase (t 1 = 0.2) ( Figure 5b). Then, we analyzed the DOS along three paths of the ART in the (t 1 , t 2 ) space ( Figure 5c). In the case of path 1 (Figure 5d), cumulative VB bending (ΔE V ) and CB bending (ΔE C ) in anatise can reach +0.41 and +0.69 eV, respectively (t 1 = t 2 = 0.8), which are sufficient to promote efficient separation of photoexcited electrons to regions with lower E C and holes to regions of higher E V (Figure 5d), leading to higher photoactivity than that of the flat-band anatase. Qualitatively similar band bending profiles are found for paths 2 and 3 ( Figure S10, Supporting Information), which confirms the formation of anatise phase as the driver for the high photoactivity of P25.
To test these conclusions ( Figure 5), we conducted highresolution X-ray photoelectron spectroscopy (XPS) to determine the average band offsets based on core-level shifts, following a previously reported method [31] (see Supporting Information for details). XPS peak fitting (Figure 6a) for the 700 °C/20 min sample shows that, on average, E V (AI) is higher than E V (A) by ΔE V = 0.12 eV (Figure 6b) and the CB minimum in anatise shifts higher than that in anatase by ΔE C = 0.37 eV ( Figure 6b; Figure S11, Supporting Information). For comparison, the measured band edge shifts for the other samples are ΔE V = 0.21 eV and ΔE C = 0.46 eV (700 °C/120 min) and ΔE V = 0.17 eV and ΔE C = 0.42 eV (P25) (see Figure S11, Supporting Information). The signs and magnitudes of the average energy shifts obtained from XPS are consistent with the band bending obtained in our simulations (Figure 5d) of maximum ΔE V = 0.41 eV and ΔE C = 0.69 eV. The band edge profiles calculated and measured for the combined anatase/anatise system consistently suggest upward band bending by a few tenths of eV in anatise, favoring transfer of photoexcited electrons to anatase and photoexcited holes to anatise. In addition, the changes from one atomic plane to another are free of electronhole recombination centers, such as defects and grain boundaries. [29] Both factors facilitate the transfer of electrons and holes in the opposite directions (Figure 6c,d) and thus inhibit their recombination. These results are consistent with a previous report that the energy barrier for electron-transfer reaction in P25 is negligible (<8.3 × 10 −4 eV). [6a] Finally, we note that the calculated bandgap of anatise ( Figure S11f,g, Supporting Information) is higher than those of both rutile and anatase, consistent with the slight blue shift of UV-vis absorption of P25 ( Figure S11h, Supporting Information) with respect to the UV-vis spectra of anatase and rutile. In summary, structural characteristics, changes of the core-level line shapes, and UV-vis spectra of anatise observed Figure 5. Band bending in anatise. a) Atomic structure of a supercell composed of two anatise phases represented by deformation parameters t 1 and t 2 . b) Example of DOS projected on the atomic planes of one supercell combining anatise two phases: t 1 = 0.2, t 2 = 0.8. c) Potential energy surface for the anatise in the range of t 1 and t 2 where it is stable or metastable, i.e., does not spontaneously transform to rutile. d) DOS projected on atomic planes of anatise for gradually increasing deformation magnitude along Path 1 (yellow line in (c)) representing observed deformation fields (see Figure 2a).

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experimentally are consistent with the simulated atomistic structure, band bending, and bandgap changes, suggesting that our model system well represent the observed anatise gradient structures.

Conclusion
Here, we report a new anatase to rutile phase transformation pathway defined by [010] A -to-[111] R and (004) A -to-(011) R . During this transformation, one out of six bonds breaks and reforms in each TiO 6 octahedron with the ART barrier of 0.62 eV per TiO 2 formula unit. This phase transformation pathway induces the formation of twin structures. The dominant type of the structural defect is a gradual and continuous transition from anatase to a highly distorted anatase phase, defined as anatise, over regions tens of nanometers in size. Our analysis of simulated XRD patterns for these continuously distorted structures shows that these patterns are indistinguishable from those of either anatase or rutile, explaining why these gradient structures remained unreported to date.
We demonstrate that the band bending, induced by the distorted but defect-free gradient structures, favors the efficient separation of electron-hole pairs and is responsible for improved photocatalytic efficiency of heat-treated TiO 2 (700 °C/20 min and 700 °C/120 min samples) as well as for the high-level photoactivity of P25. While all samples exhibit gradient structures (Figures 2 and 4), P25 has the highest activity, which we attribute to the small anatise domain size, high surface area, and a high volume fraction of the anatise phase (Figure 4k and Table 1). We have found similar transitional structures form during phase transformation from TiO 2 -B phase to anatase and substantially increase the photoactivity. [20] Charge separation in such gradient structures is fundamentally different from that at staggered band offset interfaces between two different materials or different polymorphs of the same composition. Future research deepening our understanding of the factors that drive the formation of such gradient structures offers a new avenue of controlling functional properties without the need for compositional complexity associated with interfaces. Enabling control of lattice deformation and corresponding electronic structure changes defines a method of material design to improve properties or induce new functions that takes advantage of transitional structures during transformation processes, including, but not limited to, phase transformations.

Experimental Section
Anatase particles with various sizes (≈5-200 nm, Figure S1, Supporting Information) were synthesized through hydrothermal and previously reported methods. [32] The as-prepared small anatase samples (with comparable surface area to P25) were heated in a furnace (Vulcan 3-550, Neytech) under an air environment at 700 °C for 20 min, and 700 °C for 120 min, respectively, and their photoactivity were tested via water splitting and degradation of methylene blue. For the phase transformation study, large anatase nanorods (≈100-200 nm) were employed for ease of tracking single particles during in situ studies. To avoid electron beam effects at high temperatures, semi-in situ heating TEM experiments were employed, in which the temperature was increased for phase transformation but decreased to room temperature for imaging ( Figure S1g, Supporting Information). The samples mounted into the heating holder were kept in the TEM vacuum column during the whole ART process. X-ray photoelectron spectroscopy was carried out to estimate the band offsets of samples using a Physical Electronics Quantera Scanning X-ray Microprobe, equipped with a detection system with a 32-element multichannel analyzer. Simulations using density functional theory were used to examine the potential energy surface for the anatase to rutile phase transformation and the corresponding electronic structure modifications. Calculations were performed using the VASP code.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.